Investigation of patient-sharing networks using a Bayesian network model selection approach for congruence class models.

A Bayesian approach to conduct network model selection is presented for a general class of network models referred to as the congruence class models (CCMs). CCMs form a broad class that includes as special cases several common network models, such as the Erdős-Rényi-Gilbert model, stochastic block model, and many exponential random graph models. Due to the range of models that can be specified as CCMs, our proposed method is better able to select models consistent with generative mechanisms associated with observed networks than are current approaches. In addition, our approach allows for incorporation of prior information. We illustrate the use of this approach to select among several different proposed mechanisms for the structure of patient-sharing networks; such networks have been found to be associated with the cost and quality of medical care. We found evidence in support of heterogeneity in sociality but not selective mixing by provider type or degree.